Question -
Answer -
Given: Three coins aretossed.
When three coins aretossed, then the sample space is
S = {HHH, HHT, HTH,HTT, THH, THT, TTH, TTT}
Now, the subparts are:
(i) The two eventswhich are mutually exclusive are when,
A: getting no tails
B: getting no heads
Then, A = {HHH} and B= {TTT}
So, the intersectionof this set will be null. Or, the sets are disjoint.
(ii) Three eventswhich are mutually exclusive and exhaustive are:
A: getting no heads
B: getting exactly onehead
C: getting at leasttwo head
So, A = {TTT} B ={TTH, THT, HTT} and C = {HHH, HHT, HTH, THH}
Since, A ⋃ B = B ⋂ C = C ⋂ A = Փ and
A⋃ B⋃ C = S
(iii) The two eventsthat are not mutually exclusive are:
A: getting three heads
B: getting at least 2heads
So, A = {HHH} B ={HHH, HHT, HTH, THH}
Hence, A ⋂ B = {HHH} = Փ
(iv) The two eventswhich are mutually exclusive but not exhaustive are:
A: getting exactly onehead
B: getting exactly onetail
So, A = {HTT, THT,TTH} and B = {HHT, HTH, THH}
It is because A ⋂ B = Փ but A⋃ B ≠ S